On redundancy vs dependency preservation in normalization
Why this work is in the frame
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Bibliographic record
Abstract
A recently introduced information-theoretic approach to analyzing redundancies in database design was used to justify normal forms like BCNF that completely eliminate redundancies. The main notion is that of an information content of each datum in an instance (which is a number in [0,1]): the closer to 1, the less redundancy it carries. In practice, however, one usually settles for 3NF which, unlike BCNF, may not eliminate all redundancies but always guarantees dependency preservation.In this paper we use the information-theoretic approach to prove that 3NF is the best normal form if one needs to achieve dependency preservation. For each dependency-preserving normal form, we define the price of dependency preservation as an information-theoretic measure of redundancy that gets introduced to compensate for dependency preservation. This is a number in the [0,1] range: the smaller it is, the less redundancy a normal form guarantees. We prove that for every dependency-preserving normal form, the price of dependency preservation is at least 1/2, and it is precisely 1/2 for 3NF. Hence, 3NF has the least amount of redundancy among all dependency-preserving normal forms. We also show that, information-theoretically, unnormalized schemas have at least twice the amount of redundancy than schemas in 3NF.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it